Question

Find a rational number between $\frac{1}{4}$ and $\frac{1}{3}$.

Answer 1

Compute the required number.

A rational number is a type of real numbers that can be expressed in the $\frac{p}{q}$ form where $q\ne 0$.

If we multiply, add or subtract any two rational numbers, the outcome is always a rational number.

We know that if $m$ and $n$ be two rational numbers such that $p<q$ then $\frac{1}{2}\left(p+q\right)$ is a rational number between $p$ and $q$.

Thus the rational number between $\frac{1}{4}$ and $\frac{1}{3}$ is.

$\begin{array}{rcl}\frac{1}{2}\left(\frac{1}{4}+\frac{1}{3}\right)& =& \frac{1}{2}\left(\frac{3+4}{12}\right)\\ & =& \frac{1}{2}\left(\frac{7}{12}\right)\\ & =& \frac{7}{24}\end{array}$

Hence a rational number between $\frac{1}{4}$ and $\frac{1}{3}$ is $\frac{7}{24}$.